Firebase authentication in Chrome Extension popup

I'm trying to get authentication (email/password) to work in a Chrome Extension. I seems to work just fine if I put my authentication code in the background script. However I can't seem to get it to work as a browser action script.

That example chrome extension hasn't been updated in 3 years, so its version of Firebase is out-of-date. Replace https://cdn.firebase.com/v0/firebase.js with https://cdn.firebase.com/js/client/2.2.1/firebase.js in browser_action.html and you should be able to use authWithPassword successfully.